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Implementation in mixed Nash equilibrium
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Mezzetti, Claudio and Renou, Ludovic (2009) Implementation in mixed Nash equilibrium. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.902).

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Abstract
A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of foptimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak setmonotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.
Item Type:  Working or Discussion Paper (Working Paper) 

Subjects:  H Social Sciences > HB Economic Theory 
Divisions:  Faculty of Social Sciences > Economics 
Library of Congress Subject Headings (LCSH):  Noncooperative games (Mathematics), Equilibrium (Economics), Game theory, Social choice 
Series Name:  Warwick economic research papers 
Publisher:  University of Warwick, Department of Economics 
Place of Publication:  Coventry 
Official Date:  28 April 2009 
Number:  No.902 
Number of Pages:  29 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
References:  [1] Dilip Abreu and Arunava Sen, 1991, “Virtual Implementation in Nash Equilibrium,” 
URI:  http://wrap.warwick.ac.uk/id/eprint/1315 
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